Equations Involving Division

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Year 7 Interactive Maths - Second Edition

Equations Involving Division

Consider the equation

Clearly both the left-hand side and right-hand side equal 10. That is LHS = RHS

If we double the weight on both sides, then we obtain:

The left-hand side and the right-hand side both equal 20. Therefore, LHS = RHS

We notice that the statement

remains a true statement when each side of the equation is multiplied by 2.

This suggests that equations behave like balances. If the same number multiplies the mass in both scales of a balance, it still remains balanced. This implies that we can multiply both sides of an equation by the same number to get a new equation.

If you put x/2 kg in one of a pair of scales and add 9 kg to the other, the scales will show that x/2 kg is equal to 9 kg. That is x/2 = 9

After doubling the weight in both scales, the scales remain balanced.

From the preceding discussion, we can state that:

To solve an equation, we can multiply both sides of an equation by the same number.

Example 6

Solution:

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